Numerical differentiation of implicitly defined curves

Muhammed I. Syam; Hani I. Siyyam

doi:10.1016/S0377-0427(99)00106-5

Numerical differentiation of implicitly defined curves

Muhammed I. Syam, Hani I. Siyyam

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

In this paper we develop a finite differencing device to calculate approximations of derivatives c′(0),c″(0),... of regular solution curves c:R∋s→c(s)∈Rⁿ of nonlinear systems of equations f(x)=0,f∈C^k(Rⁿ⁺¹,Rⁿ) without having to compute points on the solution curve c(s). The derivative vectors c′(0),c″(0),... can be used in the numerical approximation of the solution set f^-1(0) to construct higher-order predictors to be used in the predictor-corrector continuation method.

Original language	English
Pages (from-to)	131-144
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	108
Issue number	1-2
DOIs	https://doi.org/10.1016/S0377-0427(99)00106-5
Publication status	Published - Aug 15 1999

Keywords

Continuation method
Implicitly defined curve* Higher order predictor
Numerical differentiation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/S0377-0427(99)00106-5

Cite this

@article{7b96ff987a014a118208fd1be991c9de,

title = "Numerical differentiation of implicitly defined curves",

abstract = "In this paper we develop a finite differencing device to calculate approximations of derivatives c′(0),c″(0),... of regular solution curves c:R∋s→c(s)∈Rn of nonlinear systems of equations f(x)=0,f∈Ck(Rn+1,Rn) without having to compute points on the solution curve c(s). The derivative vectors c′(0),c″(0),... can be used in the numerical approximation of the solution set f-1(0) to construct higher-order predictors to be used in the predictor-corrector continuation method.",

keywords = "Continuation method, Implicitly defined curve* Higher order predictor, Numerical differentiation",

author = "Syam, {Muhammed I.} and Siyyam, {Hani I.}",

year = "1999",

month = aug,

day = "15",

doi = "10.1016/S0377-0427(99)00106-5",

language = "English",

volume = "108",

pages = "131--144",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier",

number = "1-2",

}

TY - JOUR

T1 - Numerical differentiation of implicitly defined curves

AU - Syam, Muhammed I.

AU - Siyyam, Hani I.

PY - 1999/8/15

Y1 - 1999/8/15

N2 - In this paper we develop a finite differencing device to calculate approximations of derivatives c′(0),c″(0),... of regular solution curves c:R∋s→c(s)∈Rn of nonlinear systems of equations f(x)=0,f∈Ck(Rn+1,Rn) without having to compute points on the solution curve c(s). The derivative vectors c′(0),c″(0),... can be used in the numerical approximation of the solution set f-1(0) to construct higher-order predictors to be used in the predictor-corrector continuation method.

AB - In this paper we develop a finite differencing device to calculate approximations of derivatives c′(0),c″(0),... of regular solution curves c:R∋s→c(s)∈Rn of nonlinear systems of equations f(x)=0,f∈Ck(Rn+1,Rn) without having to compute points on the solution curve c(s). The derivative vectors c′(0),c″(0),... can be used in the numerical approximation of the solution set f-1(0) to construct higher-order predictors to be used in the predictor-corrector continuation method.

KW - Continuation method

KW - Implicitly defined curve Higher order predictor

KW - Numerical differentiation

UR - http://www.scopus.com/inward/record.url?scp=0032613640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032613640&partnerID=8YFLogxK

U2 - 10.1016/S0377-0427(99)00106-5

DO - 10.1016/S0377-0427(99)00106-5

M3 - Article

AN - SCOPUS:0032613640

SN - 0377-0427

VL - 108

SP - 131

EP - 144

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1-2

ER -

Numerical differentiation of implicitly defined curves

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this